I don't think Scorched Earth was the first tank game, pretty sure I can recall playing simpler version (without choice of weapons) on early IBM compatibles. If worms owes something to Scorched Earth, it owes as much or more to Lemmings.
I'm glad someone else mentioned Scorched Earth. My friends and I played this to death when we were young. I never got on the Worms bandwagon though as it just felt like an over-animated very of Scorched Earth.
Worms is obviously in the same genre but it does change quite a bit - most obviously the focus on moving your team members (SE is mostly about weapon selection and aiming, in worms each turn also includes a movement phase which is just as important as the other 2 elements).
This changes the gameplay quite a bit, especially in multiplayer (it become a lot less "chess-like" and more action-y, despite being a turn based game).
I never played worms, but I saw other people play it at the height of its popularity. After seeing it mentioned on HN today I was telling my SO about it, and compared it to scorched earth. Nice to see someone else making the comparison.